Question

Suppose you start with one liter of vinegar and repeatedly remove 0.11 l, replace with water, mix, and repeat. What will be the volume of vinegar left after 5 repetitions?

1) 0.61 l
2) 0.65 l
3) 0.69 l
4) 0.73 l

Answer 1

After removing 0.11 liters of vinegar and replacing it with water 5 times, using the exponential decay formula, the remaining volume of vinegar is approximately 0.59 liters, which is closest to the 0.59 L mark, not matching any provided answer options.

Step-by-step explanation:

To calculate the volume of vinegar left after each repetition of removing 0.11 liters and replacing it with water, you need to apply exponential decay. Initially, you have 1 liter of vinegar. Each time you remove 0.11 liters and replace it with water, you are left with 0.89 liters of the original vinegar concentration. After 5 repetitions, you calculate the remaining volume using the formula: Vn = V0 × (1 - fraction removed)^n, where V0 is the initial volume and n is the number of repetitions. The formula yields V5 = 1 × (0.89)^5.

Concisely, the volume of vinegar left after 5 repetitions is V5 = 0.5934 liters, which rounds to 0.59 liters. Therefore, none of the provided answer options are correct. The actual remaining volume is closest to the 0.59 L mark.